Análise geometricamente não linear de treliças planas

Abstract

This work presents the development of a computational code in the MATLAB language for geometrically nonlinear analysis of plane trusses. This development was based on a formulation for geometrically nonlinear analysis of plane trusses through the direct stiffness method and the implementation of the Newton-Raphson method with load increments for the solution of the nonlinear equations system that represents the load-displacement relations derived by the aforementioned formulation. The code was then numerically tested through examples found in the literature and comparison of results. Good agrément was noticed between the results of nodal displacements and axial forces in the bars obtained through the code developed by the author and the results available in the literature. In examples 1 and 2, the trusses analyzed underwent the instability effect known as "snap-through" and it was possible to observe the structural behaviour and the influence of such effect on the number of iterations needed for analysis convergence. In example 4, the validity of the linear analysis for structures that undergo small displacements could be noted by comparing the results with a geometrically nonlinear analysis.